We report exotic hybrid rogue wave and breather solutions for a complex
mKdV equation describing soliton dynamics in shallow water wave and
optics. Starting from the Lax pair, the higher-order Darboux
transformations for the equation are constructed. Further, we obtain a
series of theorems to compute the hybrid rogue wave and breather
solutions. We also demonstrate the interaction features between rogue
waves and breathers by controlling parameters. These results are of
importance to understand nonlinear wave dynamics in water wave systems.